List questions from sobolev-spaces

34

Views

Is $C_\mathrm{c}^\infty (\mathbb R^d \setminus \lbrace 0 \rbrace ) \subset H^{m,p}(\mathbb R^d )$ dense?

Published on 12 Apr 2026 - 16:56

151

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Fourier series approximation of $f \in H_p^s$ rate of convergence

Published on 11 Apr 2026 - 5:32

220

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Frechet differentiability of superposition map from $H^1(\Omega)$ into its dual

Published on 29 Mar 2026 - 12:12

255

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Properties of the trace operator

Published on 08 Apr 2026 - 19:02

3.1k

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Inner product in Sobolev spaces

Published on 12 Apr 2026 - 2:48

818

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Critical Sobolev exponent

Published on 14 Apr 2026 - 17:29

65

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Why is this function in $W^{1,p}$?

Published on 17 Apr 2026 - 7:12

669

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The characteristic function of a bounded open subset of $\mathbb{R}^{n}$ is not in $W^{1,1}(\mathbb{R}^{n})$

Published on 29 Mar 2026 - 3:35

61

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How can I show the following relation on $H_{0}^{1}(U)$?

Published on 12 Apr 2026 - 21:48

556

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What boundary conditions would provide a weak solution to the problem $\Delta^2u =f$ in the space $H_0^1\cap H^2(U)$?

Published on 14 Apr 2026 - 16:43

42

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An optimal embedding result concerning Orlicz spaces

Published on 25 Mar 2026 - 7:41

96

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Compact embedding in $L^2((0,\infty),rdr)$

Published on 14 Apr 2026 - 0:41

60

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How to deflate a differential operator

Published on 09 Apr 2026 - 15:44

199

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A priori estimate of an inhomogeneous p-Laplace equation with Dirichlet boundary condition

Published on 12 Apr 2026 - 19:27

86

Views

Are piecewise constants in the bidual space of $H^{1/2}(\partial\Omega)$?

Published on 28 Mar 2026 - 1:07

List Question

Is $C_\mathrm{c}^\infty (\mathbb R^d \setminus \lbrace 0 \rbrace ) \subset H^{m,p}(\mathbb R^d )$ dense?

Fourier series approximation of $f \in H_p^s$ rate of convergence

Frechet differentiability of superposition map from $H^1(\Omega)$ into its dual

Properties of the trace operator

Inner product in Sobolev spaces

Critical Sobolev exponent

Why is this function in $W^{1,p}$?

The characteristic function of a bounded open subset of $\mathbb{R}^{n}$ is not in $W^{1,1}(\mathbb{R}^{n})$

How can I show the following relation on $H_{0}^{1}(U)$?

What boundary conditions would provide a weak solution to the problem $\Delta^2u =f$ in the space $H_0^1\cap H^2(U)$?

An optimal embedding result concerning Orlicz spaces

Compact embedding in $L^2((0,\infty),rdr)$

How to deflate a differential operator

A priori estimate of an inhomogeneous p-Laplace equation with Dirichlet boundary condition

Are piecewise constants in the bidual space of $H^{1/2}(\partial\Omega)$?

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